Question

If a stretched string which is fixed at both ends has m nodes then calculate its length​

Answer 1

Answer:

The speed vv of a wave along a string with tension TT and mass per unit length μμ is given by

v=Tμ−−√v=Tμ

T=49T=49 N and μ=0.04/8=1/200μ=0.04/8=1/200 kg/m

v=9800−−−−√≈100v=9800≈100 m/s

Now on the string, a node will always be found at each end.

Let xx be the position of a node along the string.

Now let xx be the position of antinodes

Answer 2

The length of the stretched string is $\dfrac{m\lambda}{2}$

Explanation:

We know that,

The length of the stretched string is equal to the number of node multiply by $\dfrac{\lambda}{2}$.

For one node,

$L_{1}=\dfrac{\lambda}{2}$

For one node,

$L_{2}=\dfrac{2\lambda}{2}$

$L_{2}=\lambda$

Similarly ,

For m nodes,

$L_{m}=\dfrac{m\lambda}{2}$

Hence, The length of the stretched string is $\dfrac{m\lambda}{2}$

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Topic : length of string

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